The Bizarre Quantum Nature of Light

1. The Bizarre Quantum Nature ofLight Nergis MavalvalaMassachusetts Institute of TechnologyAugust 2005

2. Einstein’s Annus Mirabilis • 1905 • Photoelectric effect • Special theory of relativity • 1916 • General theory of relativity • 1922 • Nobel prize for the photoelectric effect • 1935 • Einstein-Podolsky-Rosen (EPR) paradox

3. Schizophrenic light

4. Origins: what is light? • Is it a particle or is it a wave? • Newton in 1600s • Particles – corpuscles • Huygens in 1600s • Waves – diffraction and interference • Maxwell (1800s) • Unified laws of electromagnetism • Waves fit naturally in Maxwell’s equations

5. Experimental Observations:Confusion • Interference (Young, 1805) • Atomic spectra (1880s onward) • Black body radiation(Planck, 1900) • Photoelectric effect (Einstein, 1905) Courtesy U. Winni[peg

6. Experimental Observations:Confusion White light passing through prism • Interference (Young, 1805) • Atomic spectra (1880s onward) • Blackbody radiation(Planck, 1900) • Photoelectric effect (Einstein, 1905) Continuous spectrum Courtesy of NASA Atomic spectra  discrete lines Courtesy of Solar Survey Archive

7. Vs ω Experimental Observations:Confusion • Interference (Young, 1805) • Atomic spectra (1880s onward) • Blackbody radiation(Planck, 1900) • Photoelectric effect (Einstein, 1905) AMMETER EMITTER BATTERY(V) COLLECTOR eVs = ω- W

8. Wave/particle duality • The same entity can sometimes behave like a particle and sometimes like a wave • Wave nature • Continuous • Interference and diffraction • Particle nature • Discrete • Spectral lines...

9. Matter Waves • Louis de Broglie (1924) • Why should light be special? • All particles have wave-like properties as well • Wavelength = h ÷ (Mass x velocity) = h ÷ momentum • Davisson-Germer (1927) • Diffraction of electrons from a Ni crystal • Jönnson (1961, Tübingen) • Two slit experiment with electron beam  interference • Single electron interference (1989, Hitachi)

10. Interference of Matter Waves Courtesy of Hitachi

11. Journey into the Quantum World

12. Heisenberg Uncertainty Principle • Important consequence of the wave-particle duality • It is not possible to simultaneously measure the position and momentum (velocity) of a particle with arbitrarily high precision • The more precisely the position is known, the less well the momentum is known • Measurement of the position “kicks” the particle • The “kick” perturbs the particle’s velocity randomly • Subsequent position measurement is imprecise (back-action)

13. Heisenberg Uncertainty Principle • Try to measure position of a particle • Find that it is somewhere within an “error box” • The measurement confines the particle’s wave to be within that error box • The confined wave is made up of a superposition of wavelengths • The more confined the wave, the faster the oscillations – or shorter the wavelength – that can fit in the box (Fourier) • Momentum = h/l momentum range becomes very large

14. Quantum speed trap Do you know how fast you were going, sir? Nein, officer, but I know exactly where I am.

15. Heisenberg Uncertainty Principle • No measurement can be completely deterministic in two non-commuting observables • E.g. position and momentum of a particle • Similarly for the electromagnetic field QuadraturesAssociated with amplitude and phase

16. ½A 0 A 50% ½A LASER 50% BS Measuring the vacuum

17. Classical oscillator (continuous spectrum) Quantum oscillator (discrete spectrum) Energy E = ½ k x2 k x x Position from equilibrium Energy of harmonic oscillators

18. Classical oscillator (continuous spectrum) Quantum oscillator (discrete spectrum) Potential energyof form kx2 Energy En = (n+½) ω Transitionenergy ω n = 3 n = 2 n = 1 E0 = ½ω n = 0 x Inter-particle separation Energy of harmonic oscillators

19. Vacuum fluctuations • Vacuum is not empty • Comprised of virtual pairs of particles that are created and annihilated on time-scales determined by the Heisenberg Uncertainty (DE.Dt  ) • The so-called zero-point energy is not some infinite energy source • The zero energy state is not accessible • The lowest (ground) state is the state

20. Quantum correlationsEntangled StatesSqueezed StatesQuantum Teleporters

21. Quantum Entanglement • Can prepare particles in quantum states such that the state of particle 1 depends on the quantum state of particle 2 even though they may be spatially separated • Two electrons, A and B, each with possible spin states ↑ and ↓ (along the z-axis, e.g.) • States of A are and : • States of B are and : • The quantum state of the composite system can be such that it is a quantum superposition (‘super-correlated’) of the component systems

22. Entangled states • Classical analog • Two coins • Flip coin 1 • Could be Heads or Tails with a 50-50 probability • Flip coin 2 • Could be Heads or Tails with 50-50 probability regardless of the state of the first coin • Unless we ‘rig’ the outcome (e.g. magnetize the coins) • But the correlation between components of an entangled state is greater than classical probabilty would predict

23. Alice measures VA • The quantum state ‘collapses’ into state • Bob will measure HB with 100% probability • Alice measures HA • The quantum state ‘collapses’ into state • Bob will measure VB with 100% probability Measurement with entangled states Unknown source of entangled photons ALICE BOB PolarizationAnalyzer (H/V) PolarizationAnalyzer (H/V)

24. “Spooky action at a distance” • Einstein-Podolsky-Rosen paradox • Proposed as an attack on quantum theory in 1935 • That measurements performed with an entangled state can have an instantaneous influence on another one very far away violates • ‘Objective realism’ – Alice’s decision to measure along a given axis is ‘felt’ by Bob far away • ‘Local determinism’– physical processes occurring in one place should not depend on what’s happening some other place far away • Action at a distance historically a dilemma • Newton worried about this • How can distant objects exert forces on each other over large physical separations? • Einstein proposed a solution • Space-time curvature

25. Quantum Teleportation • Sci-fi  an object disintegrates in one place and a perfect replica reappears elsewhere • Heisenberg  exact replica requires perfectly ‘scanning’ the object, but that would destroy its state completely • EPR correlation (a type of entangled state) can circumvent this by the way quantum information is encoded

26. Other applications • Quantum cryptography • Use entangled states to transmit signals that cannot be eavesdroppped without leaving a trace • E.g. Bob and can randomly switch measurement basis (change the encryption key) • Quantum computation • Use entangled state to perform computations in parallel, allowing for faster computations • Fewer parameters required to characterize entangled ‘qubits’

27. Quantum states of light • Can prepare quantum state such that DX+DX-≥ 1 but DX+≠DX- • Phasor analogy • Stick  dc term • Ball  fluctuations • Common states • Coherent state • Vacuum state • Amplitude squeezed state • Phase squeezed state McKenzie

28. Quantum Non-Demolition(QND)

29. Quantum Non-demolition • Broad class of quantum measurements where measurement back-action is evaded • E.g., by measuring of an observable that does not effect a later measurement • QND variables (observables) • Momentum of a particle • Quadrature fields • Spin states

30. Laser Interferometers for Gravitational-wave Detection

31. Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO • Detection confidence • Source polarization • Sky location LISA

32. AstrophysicalGW source Gravitational Wave Interferometers Effect of GW on ‘test’ masses Interferometric measurement

33. GW Interferometer Measurement • How to measure the gravitational-wave? • Measure the displacements of the mirrors of the interferometer by measuring the phase shifts of the light • What makes it hard? • GW amplitude is small • External forces also push the mirrors around • Laser light has quantum fluctuations in its phase and amplitude

34. Quantum Limit in Gravitation Wave Interferometers

35. Suppose the GW signal is in the phase quadrature Vacuum fluctuations enter unused port  noise Inject phase-squeezed state to replace vacuum state X- X- X- X+ X- X+ X+ X+ Squeezed input vacuum state in Michelson Interferometer • Reduce noise Increase ratio of signal to noise

36. Initial LIGO

37. Sub-Quantum Interferometers

38. X- X+ Future GW interferometer Narrowband Broadband BroadbandSqueezed Quantum correlations Input squeezing

39. Experiments? Interferometers with Squeezing K.McKenzie et al. Phys. Rev. Lett., 88 231102 (2002)

40. How to squeeze and entangle?

41. Correlate quadratures • Make noise in each quadrature not independent of each other • (Nonlinear) coupling process needed • Squeezed states of light and vacuum • Nonlinear optical media, e.g. LiNbO3 crystals, are most commonly used • Other methods too...

42. SQZ EPRentangled SQZ Generation of Squeezed Vacuumin Optical Parametric Oscillation (OPO) B. Buchler OPO crystal (MgO:LiNbO3)

43. Typical Experimental Setup

44. Closing remarks • Light must obey the laws of quantum mechanics, including the Heisenberg Uncertainly Principle (HUP) • HUP limits the sensitivity of measurements that use light, e.g. gravitational-wave detectors • Quantum non-demolition (QND) techniques allow manipulation of the light noise without violating the HUP • Squeezed states, e.g. • Such techniques can be used in future instruments to make more sensitive measurements

45. The END

46. Some Quantum VIPs • Planck (blackbody radiation, 1900) • Bohr (hydrogen atom, 1913) • Schrödinger (wave equation, 1926) • Heisenberg (uncertainty principle, 1925) • De Broglie (particles waves, 1924) • Dirac • Pauli • Born

47. Physics and Philosophy of the Heisenberg Uncertainty Principle

48. Heisenberg Uncertainty Principle de Broglie wavelength Fourier superposition

49. Deterministic world • Polarized wave incident on a polarizer oriented at q • Maxwell’s equations  transmission through polarizer  cos2(q) • If q = 45°, 50% (½) of the wave is transmitted

50. Probabilistic world • Stream of photons incident on the same polarizer • Reduce intensity (number of photons) till one photon at a time arrives at polarizer • Can’t chop photon in half, so each photon is either transmitted or not • Polarizer cannot distinguish one photon from the next, so how does it decide? • 50-50 chance that any given photon will be transmitted • On average, half the photons get through and half don’t • For a particular photon to get transmitted, the probability 0.5 (or cos2(q) for polarizer at q)